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Both the roots of the equation (x-b)(x-c...

Both the roots of the equation `(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0` are always a. positive b. real c. negative d. none of these

A

`a + bomega +comega^(2) =0`

B

`a+bomega^(2)+comega=0`

C

`a^(2)+b^(2)+c^(2)-ab-bc-ca=0`

D

a+b+c=0

Text Solution

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The correct Answer is:
D
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AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
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  4. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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  5. If arg z = pi/4 ,then

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  6. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

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  7. The least value of p for which the two curves argz=pi/6 and |z-2sqrt(...

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  8. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  9. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

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  10. If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omeg...

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  11. If z=(sqrt(3)-i)/2, where i=sqrt(-1), then (i^(101)+z^(101))^(103) equ...

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  12. The region of the complex plane for which |(z-a)/(z+veca)|=1,(Re(a) !=...

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  13. If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the loc...

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  14. In z is a complex number stisfying |2008z-1|= 2008|z-2|, then locus z ...

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  15. The locus of the points z satisfying the condition arg ((z-1)/(z+1))=p...

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  16. the locus of z=i+2exp(i(theta+pi/4)) is

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  17. If one vertex and centre of a square are z and origin then which of th...

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  18. if the complex no z1 , z2 and z3 represents the vertices of an equ...

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  19. If |z-2-3i|+|z+2-6i|=4where i=sqrt(-1),then locus of P (z) is

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  20. If z(1),z(2),z(3) and u,v,w are complex numbers represending the verti...

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